Abstract A fuzzy set approach to uncertain functions is in the focus of this paper. The uncertainty in functions entering a model, a differential equation, for instance, is represented by α-dependent sets of crisp functions, that is, α-cuts determined by an integral membership functional that is defined by means of a continuous auxiliary function whose design depends on the information the analyst has about the uncertainty. A scalar quantity of interest evaluating the model output is assumed and its membership function is inferred from the Zadeh extension principle by solving α-dependent worst- and best-case scenario problems. Two types of auxiliary functions are considered and their algorithmic advantages and disadvantages are discussed.

中文翻译：

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不确定函数的一种新的隶属函数方法

摘要 不确定函数的模糊集方法是本文的重点。进入模型的函数的不确定性，例如，微分方程，由一组依赖于 α 的清晰函数表示，即由积分隶属函数确定的 α 切分，该隶属函数由连续辅助函数定义，其设计取决于分析师掌握的有关不确定性的信息。假设一个感兴趣的标量评估模型输出，并且通过解决依赖于 α 的最坏和最好情况问题，从 Zadeh 扩展原理推断其隶属函数。考虑了两种类型的辅助函数，并讨论了它们的算法优缺点。